Construct Centroid(G),Orcenter(H),Cercumcenter(C), and Incenter(I) for the same triangle.
What rerationship can you find among G,H,C, and I or submit of them ? Exprore for many shapes of triangles.
Here is GSP file.
We can find G, H, and C are on the same line.
Can you find the rerationship C,G,and H? length? Ratio?
When the point of I is on the same line?